Combine chickpeas, shredded beets, garlic, parsley, cumin, salt, tahini, and lemon juice in a food processor.
Pulse until mixture is coarse but sticks together; add flour if mixture is too wet.
Form into small balls or patties using your hands or a small scoop.
Heat oil in a large pan over medium heat.
Cook falafel until golden and crisp on all sides, about 3–4 minutes per side.
Drain on paper towels before serving.